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September 8, 2011 Subject:
he did more than Boolean Algebra
These days George Boole is associated with Boolean logic, which is used in the design of digital computers. And indeed he is responsible for Boolean Algebra. But Boole also did pioneering work in invariant theory, and produced this book on finite difference calculus. Finite difference calculus tends to be ignored in the 21st century. Yet this is the theoretical basis for summation of series (once one gets beyond arithmetic and geometric series). Back in the 1960s I did a lot of work requiring summation of some very strange series. Finite difference calculus provided the tools to do that. At that time I used other reference books on the subject (I did not purchase this book until the early 1970s). But this book is an excellent summary of the applied side of the subject. Since the first edition of this book was 1860, obviously there are a lot of developments not included. Indeed, even by the time of the second edition (1872), some flaws were obvious. But this gives a solid foundation. It begins with generating functions, which are still the war-horse of a lot of combinatorial analysis. Admittedly there are more complete treatments of many of the topics covered, but this still remains a basic text. This will probably never be in the fore-front of research again, but it does document the basics of what was (at one time) an important area. As such, it should certainly be preserved.